Low-power large aperture adaptive lenses for smart eyeglasses

ABSTRACT

A variable focus optical device ( 100 ) can include first optically transparent membrane ( 102 ) and a second membrane ( 104 ) that at least partially define a chamber ( 106 ) retaining an optically transparent liquid. A transparent piston ( 110 ) is attached to the second membrane ( 104 ). At least one actuator ( 112   a - c ) is operatively coupled to the transparent piston ( 110 ) and configured to move to change a focal length of the variable focus optical device ( 100 ) via actuation of the transparent piston ( 110 ). Three curved bimorph actuators ( 112   a - c ) can surround and be coupled to the piston ( 110 ) for actuation of the piston ( 110 ) to generate a plano-convex or plano-concave lens via the membranes ( 102, 104 ). A smart eyeglasses system includes a pair of variable focus optical devices ( 100 ), an object distance sensor, a battery, optional eye-tracking camera(s), and a microcontroller, collectively used for purposes of sensing distance of objects and adjusting said focal length via the variable focus optical devices ( 100 ).

RELATED APPLICATIONS

This application is a continuation application of U.S. application Ser.No. 16/068,328, filed Jul. 5, 2018, which is a U.S. national stage entryof International Application No. PCT/US2017/012537, filed Jan. 6, 2017,which claims priority to U.S. Provisional Application No. 62/367,594,filed on Jul. 27, 2016, which is incorporated herein by reference, andthis application also claims priority to U.S. Provisional ApplicationNo. 62/387,854, filed on Jan. 6, 2016, which is incorporated herein byreference.

GOVERNMENT INTEREST

This invention was made with government support under Grant EB023048awarded by the National Institutes of Health. The government has certainrights in the invention.

BACKGROUND

Deterioration of vision is inevitable to all humans. By the age of fortyfive, the biological lens in our eyes starts to lose its elasticity thusproducing refractive vision errors, and the eye cannot clearly focus theimages from the outside world. The result of refractive errors isblurred vision, affecting our ability to focus on near or far objects,which is sometimes so severe that it causes visual impairment. The fourmost common vision refractive errors are: (1) myopia (nearsightedness):difficulty in seeing distant objects clearly; (2) hyperopia(farsightedness); difficulty in seeing close objects clearly; (3)astigmatism: distorted vision resulting from an irregularly curvedcornea, the clear covering of the eyeball, and (4) presbyopia, whichleads to difficulty in reading or seeing at arm's length (linked toageing and occurs almost universally). Refractive errors cannot beprevented, but they can be diagnosed by an eye examination and treatedwith corrective glasses, contact lenses, or refractive surgery.

In particular, presbyopia is the irreversible loss of the accommodativeability of the eye that occurs due to aging. Accommodation refers to theability of the eye to increase its refractive power of the crystallinelens in order to focus near objects on the retina. In the first twodecades of life accommodative amplitude has been shown to be relativelystable in the range of 7-10 diopters. By the age of fifty, accommodativeamplitude has typically decreased to about 0.50 diopters. This declineoccurs as a natural result of aging and will ultimately affect anyperson reaching sufficiently advanced age. Despite its ubiquity, theexact mechanism behind presbyopia remains unknown. Presbyopia isprimarily an inevitable, age-related condition and accordingly itsprevalence in a given population is related to the percentage ofindividuals surviving to old age. Worldwide in 2005 over 1 billionpeople were estimated to suffer from presbyopia alone.

Eyeglasses are the most common inexpensive tools for correction ofrefractive vision errors. This corrective tool is ancient and it has notbeen notably improved since the mid-1800s. Conventional eyeglasses havea number of drawbacks; most importantly they cannot fully restore thevision accommodation range of a normal eye. Corrective eyeglasses areancient devices that originated in Europe's middle ages. Most historiansbelieve that the first form of eyeglasses was produced in Italy by monksor craftsmen around 1285-1289. Reading eyeglasses were shaped like twosmall magnifying glasses and set into bone, metal, or leather mountingsthat could be balanced on the bridge of nose. The first known artisticrepresentation of the use of eyeglasses was Tommaso da Modena's paintingin 1352. The first eyeglasses could only be used to rectify hyperopiaand presbyopia. Eyeglasses for myopia appeared much later, sometime inthe early 1400's. Hinged glasses weren't made until the 1750's. Afundamental and major drawback of eyeglasses is that these devices canonly correct for the lack of accommodation at a reduced distance range;therefore, one can produce sharp full-field images for objects that areeither far or near the observer but not both. This problem has beenpartially alleviated with the use of bifocal lenses (invented by B.Franklin in 1784), multifocal and progressive lenses, which remedy thisproblem but at the expense of a reduced, fragmented field of view. Inspite of many advances in the materials and fabrication techniques foreyeglasses in the last fifty years, there has been essentially nomeaningful progress in the operation and basic limitations of thesedevices since the early 1900's.

Refractive vision errors that originate from loss or inability of eyeaccommodation (its ability to change focus) cannot be fully corrected byfixed eyeglasses. In the human eye, the image is produced at the retinawhich is immersed in vitreous humor, a watery fluid with index ofrefraction n_(t)=1.33. The lens equation for the human eye imagingsystem is approximately

$\begin{matrix}{{\frac{1}{s_{o}} + \frac{n_{t}}{s_{i}}} = {\frac{n_{t}}{f_{i}} = \frac{1}{f_{o}}}} & (1)\end{matrix}$

where s_(o) is the distance between the object and the lens, s_(i) isthe distance between the lens and image, f_(t) is the image focaldistance and f_(o) is the object medium referred focal distance. Ahealthy eye automatically adjusts the lens focal length to produce asharp image at the retina independent of the object distance. In otherwords, the eye lens object focal distance is adjusted such that

$\begin{matrix}{{f_{o}( {s_{o},s_{i}} )} = \frac{s_{o} \cdot s_{i}}{s_{i} + {n_{i} \cdot s_{o}}}} & (2)\end{matrix}$

for a fixed s_(i). The image focal length of the eye with an object atinfinity is approximately (f_(i))_(max)=s_(i)=22 mm corresponding to anobject lens power (the inverse of (f_(o))max) of +60 diopters. Thenormal eye can adjust its focal length to see objects between ˜10 cm toinfinity. Therefore (f_(i))_(min)˜19 mm corresponding to a maximumobject lens power of +70 diopters. The normal accommodation range of thehuman eye is (Delta P_(eye))_(normal)=7-10 diopters.

If the eye losses its ability to accommodate its lens focal length,objects in some regions of the 10 cm-infinity range will be projected onthe retina out of focus producing refractive errors. Conventionaleyeglasses correct these errors by placing a fixed focus lens of powerP_(lens) in close proximity of the lens between the object and the lens.For two or more thin lenses close together, the optical power of thecombined lenses is approximately equal to the sum of the optical powersof each lens: P=P1+P2. Therefore the net corrective effect isapproximately

$\begin{matrix}{ {\frac{1}{f_{o}} \approx {\frac{1}{( f_{o} )_{eye}} + P_{lens}}}arrow f_{o}  = \frac{( f_{o} )_{eye}}{1 + {P_{lens} \cdot ( f_{o} )_{eye}}}} & (3)\end{matrix}$

For presbyopia and hyperopia, 14 mm and the image is projected behindthe retina; hence we use a corrective lens with a positive power,P_(lens)>0 to bring the image at the retina back in focus. For myopia,the situation is reversed as 17 mm projecting the image in front of theretina; hence we use a corrective lens with a negative power, P_(lens)<0for focusing. Note that all that a fixed power corrective lens does isto provide a fixed shift in the effective object lens power of the eyeproduce the “in focus” focal distance of the equation immediately above.It does not change the accommodating power range of the defective eye.

$\begin{matrix}{{\Delta P_{eye}} = {( {\frac{1}{( f_{o} )_{\min}} - \frac{1}{( f_{o} )_{\max}}} ) < ( {\Delta P_{eye}} )_{normal}}} & (4)\end{matrix}$

This is the reason why a fixed focus corrective lens can bring objectswithin a range in focus, but cannot correct the focus for the entirerange of normal vision. The modern conventional approach for visioncorrection over the entire object distance range is based on theutilization of bifocal or multifocal lenses where different regions ofthe vision field have different focal lengths. For example in bifocalglasses it is common to increase the lens power on the lower half of thevisual plane for reading which fails to imaging objects over the entirevisual field. In short, it is clear that despite its ancient origins thecorrective eyeglass technology has not progressed much in theirfunctionality. Current state of the art eyeglasses do not fully restorevision, while billions of world population inevitably suffer fromdeteriorating vision.

There is a large amount of literature on the construction of variablefocus lenses. One of earliest attempts for variable focus eyeglasses hasbeen the Alvarez lens. The Alvarez lens includes twoplano-convex-concave lenses sliding against each other. Each of thecurved surfaces contributes a positive or negative power for eachinterface of the lens. The net power depends on their relative positionwhich can be adjusted to a positive or a negative power with a slider ora screw. Alvarez lenses are commercially available with adjustablepowers between −6 to +3 diopters. The Alvarez lens has unfortunatelymany visually disturbing issues including the presence of a visible gap,and imperfections and friction in the sliding glasses virtually rendersthem useless for practical situations. An additional problem with thesetypes of lenses is that the field of vision is severely reduced due tothe continuously varying lens power.

Variable focus lenses can be implemented using two additionaltechnologies. The most interesting approach is the use of liquidcrystals. The index of refraction in liquid crystal materials is afunction of their applied electric field. One may therefore implement alens simply by changing the voltage of a LCD liquid layer trappedbetween two pieces of glass. Unlike regular shaped-surface lenses, LCDvariable focus lenses are flat and are based on graded index lenses (orGRIN lenses) which are commonly used in the fiber optics industry. Thechange in the delay phase with radius is formed by the resultingelectric fields produced by a specific transparent electrode (ITO)shape. The aberration distortions produced by LCD glasses are small, andSato developed a lens arrangement that produces focusing for a widerange of light polarizations. In principle, LCD is very attractive forthis application because it takes very little electrical power to changethe phase of the light through the LCD material. This implementationmethod indeed works well for lenses a few mm in diameter used in singlewavelength light. In the eyeglass application, however, the aperture islarge. Since the LCD power is

$\begin{matrix}{P = {\frac{\lambda\Delta\phi}{\pi \cdot r^{2}} = \frac{{2 \cdot t \cdot \Delta}\; n}{r^{2}}}} & (5)\end{matrix}$

where r is the lens aperture radius, Δ is the light wavelength, Δϕ isthe change in phase, Δn is the change in index and t is the LCDthickness. Because of the quadratic radius dependence it is difficult tomake a high power large aperture LCD lenses. A proposed method to avoidexcessively large LCD thicknesses is the use of Fresnel configurations.Unfortunately, Fresnel lenses do not have sufficient image quality forpractical ophthalmic applications.

Variable focus lenses of large aperture can also be implemented usingfluidic, flexible lenses. A variable focus liquid lens includes acylindrical bladder with flexible membrane walls which is filled with atransparent optical fluid. The shape of the lens is changed by pumpingfluid in and out of the lens or by squeezing the fluid lens. Somecommercially available examples have manually adjusted liquid filledeyeglass capable of adjusting the lens power between −6 to +3 diopters.A major issue with liquid squeezable lenses is the actuation mechanismsize and weight. Several actuation approaches have been tried withvarious degrees of success, including the use of external motors,electrostatic forces, electrophoretic motion, and more recentlypiezoelectrics. The largest aperture commercially available continuouslyadjustable variable-focus liquid lens is manufactured by Optotune with aclear aperture of 20 mm, and the largest electrically tunable liquidlens has aperture of 10 mm. However, none of these lenses has sufficientaperture for commercially useful eyeglasses. Larger aperture fluidicsystems have been realized, but they are not practical for lightweightapplications without careful consideration of the storage of the lensliquid. The realization of a lightweight adjustable focus lens thatworks well for eyeglasses is still an unsolved problem.

SUMMARY

A variable focus optical device comprises a first optically transparentmembrane and a second membrane defining a chamber. An opticallytransparent liquid is disposed in the chamber. A transparent piston ispositioned adjacent and attached to the second optically transparentmembrane. At least one actuator is operatively coupled to thetransparent piston and configured, upon activation, to move thetransparent piston thereby deforming the first and second membranes tochange a focal length of the variable focus optical device.

Although other actuators may be used, in one example, the at least oneactuator can be three curved bimorph piezoelectric actuators thatsurround the transparent piston and couple the piston to a framesupporting the first and second membranes. The transparent piston, firstoptically transparent membrane, and the second membrane can each havesubstantially the same central axis. The actuators can function with anelectrical power dissipation of approximately 10 to 20 mW or lowerdepending on the driving mode (static piezo lenses consume nearly zeropower), thereby providing a very low-power lens actuator relative to asize of the lens aperture being at least 10 mm, preferably at least 30mm.

An eyeglasses system designed for ophthalmic applications comprises apair of lenses coupled to a frame, and each lens comprises a transparentpiston membrane and at least one actuator operable to move thetransparent piston membrane. An object distance sensor is coupled to theframe and configured to measure a distance from the proximate the lensesto an object. Optionally, at least one eye tracking sensor can becoupled to the frame and configured to measure at least one eye positionof a wearer. A microcontroller can also be coupled to the frame andconfigured to facilitate actuating the at least one actuator to move thetransparent piston membrane of each lens to adjust a focal length ofeach lens as corresponding to the measured distance of the object and tothe at least one eye position of the wearer. The object distance sensorcan comprise an infrared proximity sensor configured as a time-of-flightmeasurement device, and the at least one eye tracking sensor cancomprise an infrared light source and a video camera configured tomeasure eye position and eye movement.

There has thus been outlined, rather broadly, the more importantfeatures of the invention so that the detailed description thereof thatfollows may be better understood, and so that the present contributionto the art may be better appreciated. Other features of the presentinvention will become clearer from the following detailed description ofthe invention, taken with the accompanying drawings and claims, or maybe learned by the practice of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic model of a variable focus optical device inaccordance with an example of the present disclosure.

FIG. 2A is an illustration of a curved bimorph of the variable focusoptical device of FIG. 1 in accordance with an example of the presentdisclosure.

FIG. 2B is an illustration of deflection of the curved bimorph of FIG.2A in accordance with an example of the present disclosure.

FIG. 3A is a schematic cross sectional view of a variable focus opticaldevice in accordance with an example of the present disclosure.

FIG. 3B is the variable focus optical device of FIG. 3A in a convexconfiguration in accordance with an example of the present disclosure.

FIG. 3C is the variable focus optical device of FIG. 3A in a concaveconfiguration in accordance with an example of the present disclosure.

FIG. 4 is an isometric view of smart eyeglasses having variable focusoptical devices in accordance with an example of the present disclosure.

FIGS. 5A-5C are each graphs illustrating performance of a variable focusoptical device in accordance with an example of the present disclosure.

These drawings are provided to illustrate various aspects of theinvention and are not intended to be limiting of the scope in terms ofdimensions, materials, configurations, arrangements or proportionsunless otherwise limited by the claims.

DETAILED DESCRIPTION

While these exemplary embodiments are described in sufficient detail toenable those skilled in the art to practice the invention, it should beunderstood that other embodiments may be realized and that variouschanges to the invention may be made without departing from the spiritand scope of the present invention. Thus, the following more detaileddescription of the embodiments of the present invention is not intendedto limit the scope of the invention, as claimed, but is presented forpurposes of illustration only and not limitation to describe thefeatures and characteristics of the present invention, to set forth thebest mode of operation of the invention, and to sufficiently enable oneskilled in the art to practice the invention. Accordingly, the scope ofthe present invention is to be defined solely by the appended claims.

Definitions

In describing and claiming the present invention, the followingterminology will be used.

The singular forms “a,” “an,” and “the” include plural referents unlessthe context clearly dictates otherwise. Thus, for example, reference to“a bimorph” includes reference to one or more of such features andreference to “inducing” refers to one or more such steps.

As used herein with respect to an identified property or circumstance,“substantially” refers to a degree of deviation that is sufficientlysmall so as to not measurably detract from the identified property orcircumstance. The exact degree of deviation allowable may in some casesdepend on the specific context.

As used herein, “adjacent” refers to the proximity of two structures orelements. Particularly, elements that are identified as being “adjacent”may be either abutting or connected. Such elements may also be near orclose to each other without necessarily contacting each other. The exactdegree of proximity may in some cases depend on the specific context.

As used herein, a plurality of items, structural elements, compositionalelements, and/or materials may be presented in a common list forconvenience. However, these lists should be construed as though eachmember of the list is individually identified as a separate and uniquemember. Thus, no individual member of such list should be construed as ade facto equivalent of any other member of the same list solely based ontheir presentation in a common group without indications to thecontrary.

As used herein, the term “at least one of” is intended to be synonymouswith “one or more of” For example, “at least one of A, B and C”explicitly includes only A, only B, only C, or combinations of each.

Numerical data may be presented herein in a range format. It is to beunderstood that such range format is used merely for convenience andbrevity and should be interpreted flexibly to include not only thenumerical values explicitly recited as the limits of the range, but alsoto include all the individual numerical values or sub-ranges encompassedwithin that range as if each numerical value and sub-range is explicitlyrecited. For example, a numerical range of about 1 to about 4.5 shouldbe interpreted to include not only the explicitly recited limits of 1 toabout 4.5, but also to include individual numerals such as 2, 3, 4, andsub-ranges such as 1 to 3, 2 to 4, etc. The same principle applies toranges reciting only one numerical value, such as “less than about 4.5,”which should be interpreted to include all of the above-recited valuesand ranges. Further, such an interpretation should apply regardless ofthe breadth of the range or the characteristic being described.

Any steps recited in any method or process claims may be executed in anyorder and are not limited to the order presented in the claims.Means-plus-function or step-plus-function limitations will only beemployed where for a specific claim limitation all of the followingconditions are present in that limitation: a) “means for” or “step for”is expressly recited; and b) a corresponding function is expresslyrecited. The structure, material or acts that support the means-plusfunction are expressly recited in the description herein. Accordingly,the scope of the invention should be determined solely by the appendedclaims and their legal equivalents, rather than by the descriptions andexamples given herein.

Low-Power Large Aperture Adaptive Lenses for Smart Eyeglasses

In order to resolve the issues in current state-of-art eyeglasses, thepresent disclosure pertains to a new adaptive smart eyeglass thatrestores the full visual range. A component to the disclosed smartglasses system is a set of variable focus, large aperture lenses. Inorder to accommodate the needs of most eyeglass-corrected problems, thepower of the lens can have an accommodation ranging from −4 to +4diopters. Furthermore, most eyeglass lenses are light, thin, and haveaperture of 10-45 mm in diameter. Using the system herein, such variablelens power range and aperture range can be accommodated at a minimumelectrical power expense.

FIG. 1 illustrates a variable focus optical device 100 in accordancewith an example of the present disclosure. The variable focus opticaldevice 100 can be incorporated as a lens of a pair of eyeglasses, asshown and discussed regarding FIG. 4 in one example. The variable focusoptical device 100 can comprise a first optically transparent membrane102 and a second optically transparent membrane 104 defining a chamber106 (see also the discussion of FIG. 3A-3C). The optically transparentmembranes can be formed of any suitable flexible transparent material.Typically a polydimethylsiloxane (PDMS) polymer can be used, althoughnon-limiting examples can include elastomers, fluoroelastomers,saturated and non-saturated rubbers, silicone rubbers and other thinflexible polymers such as Teflon, polyethylene. If the membrane issufficiently thin its deflection can be made completely tensiondominated and independent of the mechanical properties of the membranefilm. The optically transparent membranes can generally have a thicknessranging from about 0.01 mm to about 2.0 mm and often from about 0.08 mmto about 0.4 mm, although thicknesses can vary considerably depending onmaterial strength. An optically transparent liquid 108 may be disposedin the chamber 106, thereby defining a closed fluidic lens system, forinstance. Typically, the chamber can be enclosed so as to form a closedfluid system without inlets or outlets such that during focusing thefluid volume in the chamber remains constant. During manufacture, aninlet may be provided to initially introduce fluid which is then cappedor plugged once filled. The optically transparent liquid 108 can beglycerine, or glycerol having a density of 1.26 g cm⁻³ where n=1.47, forinstance. Other suitable transparent liquids can include, but are notlimited to, high index optical fluids such as SANTOLIGHT 5267 (n=1.67)liquid crystals, ferroelectric liquids, other high index oils, and thelike. The chamber 106 can be defined by a circumferential wall 120disposed about a perimeter of the chamber 106 to contain the opticallytransparent liquid 108. The wall 120 can be part of a frame ofeyeglasses, for instance, or can be a separate wall such that a completelens unit can be inserted into a corresponding eyeglass frame. Atransparent piston 110 may be positioned adjacent and often in directcontact with the second optically transparent membrane 104. Thetransparent piston 110 can be formed of any suitable transparentmaterial having sufficient rigidity to deflect the second membrane 104.Non-limiting examples of suitable material for the transparent pistoncan include glass, polycarbonate, acrylics, sapphire, transparentceramics, and the like. As a general rule, the transparent piston canhave any thickness as long as it provides sufficient stiffness. If thepiston thickness is made too thin, the piston will deform also causing alensing effect. Generally, the piston thickness can be minimized forreduced weight and can typically range from about 0.2 mm to about 3 mm,depending on the lens size, power range, and material strength. In oneaspect, the transparent piston 110 can be bonded to the second membrane104 by a clear urethane liquid rubber so that it moves collectively withthe piston 110 when actuated. In one example, the second membrane 104spans the lens opening as a uniform continuous layer. Alternatively, thesecond membrane 104 can be formed having the transparent piston 110oriented within an aperture of the membrane. In such a case the secondmembrane 104 can be secured to edges of the transparent piston. Further,in such cases the second membrane may be transparent or can be opaquesince the second membrane would be present outside an outer perimeteredge of the transparent piston 110. The second membrane may be securedvia crimping, gluing, or any suitable fastening mechanism. When thesecond membrane 104 is secured to a perimeter of the transparent piston110, the second membrane defines a portion of the chamber, while thetransparent piston defines a remaining portion of the chamber to form anenclosed chamber.

Regardless, a plurality of actuators 112 a-c may be operatively coupledto the transparent piston 104 and configured, upon activation by anapplied voltage, to move the transparent piston 104 (in a z direction;e.g., FIGS. 3B and 3C). Thus, the first and second optically transparentmembranes 102 and 104 can be caused to deform to change a focal lengthof the variable focus optical device by changing a relative distancebetween the first and second optically transparent membranes 102 and 104and curvature of the first optically transparent membrane 102.

In one specific example, the plurality of actuators 112 a-c can be threecurved bimorph piezoelectric actuators that collectively surround thetransparent piston 110. Although three such actuators are illustrated,any functional number of such actuators may be used (e.g. two to aboutsix, and most often three to four). For example, a higher number ofactuators may limit the power accommodation range (e.g. piston movementdistance). The bimorph piezoelectric actuators can be formed by layeringa passive layer between two piezoelectric layers or by bonding twolayers of different polarization. Non-limiting examples of suitablepiezoelectric materials can include PZT, PZT-5A, PZT-5H, PMNPT,PIN-PMN-PT.

A frame 114 (such as a frame of eyeglasses or a cylindrical wall) maysupport the first and second membranes 102 and 104. Dow Corning's “734Flowable Sealant” can be used to seal the membranes 102 and 104 to theframe 114, for instance. Other suitable sealants can include, but arenot limited to, elastomer-plastic, elastomer-glass sealants, andelastomer-metal sealants The frame 114 can be one or more structuralsupport components that structurally support each membrane 102 and 104and the transparent piston 110. In any event, the frame 114 supportsannular perimeter portions of each of the first and second membranes 102and 104, thereby spatially separating them from each other about theoptically transparent liquid 108.

The actuators 112 a-c can be operatively coupled between the frame 114and the transparent piston 110. Specifically, each actuator 112 a-c canbe attached at one end (“fixed end”) to a frame support portion 116 a-c,respectively, and attached at the other end (“free end”) to a pistonconnecting portion 118 a-c, respectively. In this manner, each actuatorextends circumferentially about a portion of a perimeter of thetransparent piston. Each piston connecting portion 118 a-c can be aflange that extends outwardly from a center of the transparent piston110, and each flange can be attached to the free end of each actuator112 a-c. Each frame support portion 116 a-c is raised above or protrudesfrom the frame 114. Each frame support portion 116 a-c can have a slotor other interfacing/coupling member to fixedly attach to the fixed endof each actuator 112 a-c. Either or both of the piston connectingportions 118 a-c and frame support portions 116 a-c can be integrallyformed as part of the piston or frame, respectively, or can be attachedthereto. This configuration effectively provides a piezoelectriccantilever arrangement where each actuator 112 a-c is spatiallypositioned away from the frame 114 so that each actuator 112 a-c canbend or actuate relative to the frame 114 to move the transparent piston110 in either direction along the z axis (e.g., see FIGS. 3A-3C), whichthereby can change a focal length of the variable focus optical device100.

Alternatively, pivoting pins can be coupled between the free ends ofeach actuator 112 a-c and respective piston connecting portions 118 a-cto more freely allow flexure of the each actuator 112 a-c when actuated(thereby reducing or eliminating a bending moment of the actuated piston110 and corresponding piston connecting portions 118 a-c). For example,nickel plated steel pins can be soldered on the free end of eachactuator 112 a-c. The connecting portions 118 a-c can each have ahorizontal hole to receive a respective pin of a respective actuator.This pin and hole configuration provides a pivoting end for eachactuator, which can overcome twist-induced stiffening of the curvedactuators, thus providing improved vertical deflection of the piston 110without compromising force.

In one example, each actuator 112 a-c is curved about a perimeter of thetransparent piston 110 and congruent with a perimeter portion of theframe 114. Consequently, the actuators are curved or surround theperimeters of the first and second transparent membranes 102 and 104,and do not obstruct the transparency of the membranes 102 and 104 or thepiston 110.

This curved bimorph deformation principle is further illustrated in FIG.2A (un-deformed) and in FIG. 2B (deformed). The curved bimorph actuator200 consists of two thin-film layers, such as different piezoelectricmaterials, as known in the industry. A passive layer can also bedisposed between the two active piezoelectric layers. The difference instrains produced in the two active layers causes the bimorph to curl dueto the differential voltage between the two layers (when a voltage isapplied), thereby leading to actuation (i.e., one layer contracts whilethe other expands). In one specific example, actuator sheets provided byPiezo System, Inc. can be used (part number CT223-H4CL-503X) and cutinto curved shapes by using diamond rotary saw followed by grinding.However, such bimorph piezoelectric elements can be commerciallyobtained or directly formed.

Deflection of straight bimorphs, on the other hand, is linearlyproportional to the applied drive voltage and quadratically proportionalto the bimorph length. The theory of straight bimorphs and multimorphsis generally known. Straight bimorphs undergo bending upon actuation ina y direction. The tip deflection z of a bimorph of length L with anexternal applied opposing force F is

$\begin{matrix}{z = {\frac{L^{2}}{6 \cdot E \cdot I} \cdot ( {{3 \cdot M_{p}} - {2 \cdot F \cdot L}} )}} & (6)\end{matrix}$

where E and I are the Young modulus and moment of inertia, respectivelyand M_(p) is the piezoelectric moment

M _(p) =w·I·d ₃₁ ·t _(p) ·V  (7)

where w is the beam width, t_(p) is the thickness of each bimorph layer(generally half the bimorph thickness), d₃₁ is the piezoelectriccoefficient and V is the applied voltage.

Curved bimorphs are different from the straight bimorphs because as theybend they also rotate, as shown on FIG. 2B. The rotation is caused bythe difference in the curved bimorph length at the outer and innerradius, which results in a larger deflection on the outer radius. Thevertical and angular deflection have been calculated in

$\begin{matrix}{{{U( {r,s} )} = {\frac{M_{b} \cdot R^{2}}{E_{b} \cdot I_{b}} \cdot ( {1 - {\cos ( \frac{s}{R} )}} )}},{{\phi (s)} = \frac{U(s)}{R}},} & (8)\end{matrix}$

where U (s) is the vertical deflection at the mid radius R as a functionof the length along the mid radius, and φ(s) is the angle B, as shown inFIG. 2B. The parameters, E_(b) and I_(b) are the bimorph's Young'smodulus and moment of inertia, respectively and M_(b) is the bimorph'spiezoelectric moment,

M _(b) =w _(b) ·E _(b) ·d ₃₁ ·t _(b) ·V _(b),  (9)

where, w_(b) is the bimorph's beam width, t_(b) is the thickness of eachbimorph layer, d₃₁ is the bimorph piezoelectric coefficient, and V_(b)is the bimorph's applied voltage.

Note that for efficient deflection, the free end of the bimorph mustpivot about the highest elevation point at the end of the outer radius.As mentioned above, curved bimorphs bend and rotate when actuated, asillustrated comparing FIGS. 2A and 2B. For example, a 22.5 mm radius (R)(i.e., center radius) actuator being 5 mm wide (W) and has an angle of115 degrees (A), and upon applying a 10-20 mW voltage, then a 1 mmdeflection (C) yields a rotation angle (B) of 2.5 degrees. Thus, thedifference in deflection is approximately 20 percent between the innerand outer radius of the curved bimorph actuator 200. In the examples ofFIGS. 1 and 3A-3C, the three curved bimorph actuators can verticallydisplace about 1 mm (in either z direction) under a 50 gram load. Thisis the deflection force that can be required to move a 30-40 mm aperturelens using 20 mW (or less) of power, for example. The actuators 112 a-ccan each have a mechanical resonance of about 65-70 Hz, which isrelatively fast compared to other lens actuation systems. Such resonancecorresponds to focus response times from about 1 msec to about 5 secondsand in some cases from 15 msec to 100 msec, depending on specificconfiguration and materials used. The above example is illustrated onFIGS. 3A-3C, as further discussed below.

In one example, a curved bimorph can have the following characteristics:

TABLE 1 Bimorph Material PZT 5H4E Layer Thickness, t_(p) 270 μm Width, w8.5 mm Young's Modulus, E 5 × 10¹⁰ N/m² Piezoelectric StrainCoefficient, d₃₁ −320 × 10⁻¹² m/V Radius of Curvature, R 21.75 mm Angleof Cosine, (s/R) 110° Voltage Range 0-250 VThus, the bimorph actuators can require multiple high voltage controlsignals. For evaluation and testing purposes, a fixed 300V DC voltagesource can be converted to variable voltages using high-voltage pulsewidth modulators (PWMs). This high voltage DC can also be generatedusing miniature 3V DC-to-DC converters suitable for battery drivensetups. In one example, each PWM modulator can be implemented using ahigh voltage half-bridge driver circuit (ST Micro L6384E) and two highvoltage NMOS transistors (ST Micro IRF820) and a high-voltage 100 nFcapacitor. The half-bridge drivers can be driven by a microcontrollerthrough opto-isolators. The bimorph actuators can be driven in atwo-terminal series configuration using two PWM high-voltage circuits indifferential drive configuration. A software open loop control systemcan be used to control the bimorph deflection and the lens opticalpower. The bimorph actuator bending magnitude and direction can also bechanged by adjusting the duty cycle of the PWM signal and driving fromonly one of the opposing PWM drivers. In addition to series bimorphactuators, other more efficient three-terminal configurations are alsopossible, such as Y-poled (polling direction same) three-wire bimorphsfor actuation in a bipolar configuration. The bipolar configuration canprovide 30% more deflection with higher actuation force but can alsorequire higher voltages, sometimes as large as double the voltagerequired in the series configuration.

FIGS. 3A-3C provides a cross sectional schematic views of a variablefocus optical device 300, such as the device 100 of FIG. 1, according toan example of the present disclosure. Similarly, the variable focusoptical device 300 may include a first optically transparent membrane302 and a second optically transparent membrane 304 defining a chamber306. An optically transparent liquid 308 may be disposed in the chamber306, thereby defining a closed fluidic system. A transparent piston 310may be positioned adjacent and attached to the second opticallytransparent membrane 304, such as in the arrangement shown and describedregarding piston 110 of FIG. 1. The transparent piston 310 can beadhered to the second membrane 304 along the outer surface of the secondmembrane 304. A frame 314 supports the first and second membranes 302and 304. The frame can be a frame of eyeglasses or a circumferentialwall. The frame 314 can be comprised of a uniform rigid body supportingperimeter portions of the first and second membranes 302 and 304, or theframe 314 can be a plurality of rigid components coupled to each other.In one aspect, the transparent piston 310 and the first and secondmembranes 302 and 304 each have substantially the same central axisalong the z direction. The frame 314 can have a height of approximately2.5 mm, an inner radius of approximately 18 mm, and an outer radius ofapproximately 22 mm, in one example. However, as a general guideline,the height may range from 0.5 to 10 mm, the inner radius from 10 to 35mm, and the outer radius from 12 to 40 mm.

As shown on each of FIGS. 3B and 3C, upon actuation of at least oneactuator 312 (or three actuators, as in FIG. 1), the piston 310 movessuch that a collective shape of the first and second opticallytransparent membranes 302 and 304 increases or decreases to produceeither a plano-convex or a plano-concave shape, respectively.Specifically, configuration A of FIG. 3A shows the variable focusoptical device 300 in an un-deflected nominal shape, and configuration Bof FIG. 3B shows the variable focus optical device 300 in a plano-convexshape, and configuration C of FIG. 3C shows the variable focus opticaldevice 300 in a plano-concave shape. Thus, with regard to FIG. 3B,applying a positive voltage (e.g., of 10-20 mW) to the at least oneactuator 312 causes the actuator (being one or more curved piezoelectricbimorphs) to deflect and bend in a first direction (z direction),thereby causing the attached piston 310 to move toward and bias thesecond membrane 304. Such movement causes the second membrane 304 todeflect (relative to the frame 314), which causes fluidic pressure ofthe optically transparent liquid 308 in the chamber 306 in a pushingmanner. Such pressure of the optically transparent liquid 308 in the zdirection causes deflection of the first membrane 302, therebygenerating a plano-convex shape configuration B. This can cause apositive change in lens power over a 5-8 Diopter range, for a 32 mmdiameter aperture.

Inversely, with regard to FIG. 3C, applying a negative voltage (e.g.,10-20 mW) causes the actuator 312 (e.g., one or more curvedpiezoelectric bimorphs) to deflect and bend in a second direction (zdirection) opposite the first direction, thereby causing the attachedpiston 310 to move away from and “pull” the attached second membrane304. Such movement causes the second membrane 304 to deflect (relativeto the frame 314), which causes fluidic pressure of the opticallytransparent liquid 308 in the chamber 306 in a pulling manner. Suchdisplacement of the optically transparent liquid 308 in the (opposite) zdirection causes deflection of the first membrane 302, therebygenerating a plano-concave shape configuration C. This can cause anegative change in lens power over a 5-8 Diopter range for a 32 mmdiameter lens.

The total force required to change the lens power (e.g., a variablefocus lens device) is the sum of the force required to deflect the firstmembrane 302 and the second membrane 304 with the piston 310, forinstance. Thus, the first membrane 302 has a thickness t_(t) and radiusr_(i) and the second membrane 304 has a thickness and radius t_(b) andr_(b). The second membrane 304 radius is larger than that of the firstmembrane 302. The second membrane 304 is forced flat at the center usingthe piston 310 of radius r_(p). When a force is applied to the secondmembrane 304, the shape of the liquid lens will increase or decrease toproduce either a plano-convex of a plano-convex lens obeying equation(10).

$\begin{matrix}{P = {\frac{1}{f} = {{( {n - 1} )\lbrack {\frac{1}{R_{1}} - \frac{1}{R_{2}} + \frac{( {n - 1} )d}{nR_{1}R_{2}}} \rbrack} = \frac{( {n - 1} )}{R}}}} & (10)\end{matrix}$

Thus, the force required for the first membrane 302 (F_(top)) and thesecond membrane 304 (F_(bot)) is

$\begin{matrix}{{F_{top} = {( \frac{16{\pi \cdot E_{1}}t_{t}^{3}}{3 \cdot {r_{t}^{2}( {1 - v^{2}} )}} ) \cdot \delta_{t}}}\mspace{14mu} {F_{bot} = {( \frac{16{\pi \cdot E_{b}}t_{b}^{3}}{{3 \cdot {r_{b}^{2}( {1 - v^{2}} )}}( {1 - ( \frac{r_{p}^{4}}{r_{b}^{4}} ) - {4 \cdot ( \frac{r_{p}^{2}}{r_{b}^{2}} ) \cdot {\ln ( \frac{r_{b}}{r_{p}} )}}} )} ) \cdot \delta_{b}}}} & (11)\end{matrix}$

where E₁ and E_(b) are the Young's moduli of the first and secondmembranes 302 and 304, respectively, and δ_(t) and δ_(b) are thecorresponding peak deflections. Because the piston 310 is flat, thepower of the lens is give by equation (10), and the deflections of thefirst and second membranes 302 and 304 are connected as the total liquidvolume is constant.

$\begin{matrix}{V_{t} = {{\frac{\pi}{2} \cdot r_{t}^{2} \cdot \delta_{t} \cdot ( {1 - \frac{\delta_{t}^{2}}{3 \cdot r_{t}^{2}}} )} + {\pi \cdot r_{t}^{2} \cdot h_{t}} + {\pi \cdot r_{b}^{2} \cdot h_{b}} + {\pi \cdot r_{p}^{2} \cdot \delta_{b} \cdot ( {1 + \frac{( {r_{b} - r_{p}} )( {r_{b} + {2r_{p}}} )}{3 \cdot r_{b}^{2}}} )}}} & (16)\end{matrix}$

but also at zero deflection

V _(t) =π−·r _(t) ² ·h _(t) +π·r _(b) ² ·h _(b)  (17)

Therefore and δ_(t) and δ_(b) are approximately linearly related

$\begin{matrix}{\delta_{t} \approx {{- 2} \cdot \frac{r_{p}^{2}}{r_{t}^{2}} \cdot \delta_{b} \cdot ( {1 + \frac{( {r_{b} - r_{p}} )( {r_{b} + {2r_{p}}} )}{3 \cdot r_{b}^{2}}} )}} & (18)\end{matrix}$

and the radius of curvature of the lens is

$\begin{matrix}{R \approx \frac{r_{t}^{2}}{2 \cdot \delta_{t}}} & (19)\end{matrix}$

Therefore the lens power is

$\begin{matrix}{P \approx {{\frac{4 \cdot r_{p}^{2} \cdot \delta_{b}}{r_{t}^{4}} \cdot ( {1 + \frac{( {r_{b} - r_{p}} )( {r_{b} + {2r_{p}}} )}{3 \cdot r_{b}^{2}}} )}( {n - 1} )}} & (20)\end{matrix}$

Such force is linearly proportional to the piston deflection δ_(b) andthe piston force F_(bot). Now a calculation can be made for the forcerequired to obtain a power change of +4 diopters.

In one example, the first and second membranes 302 and 304 (e.g., beingpolydimethylsiloxane (PDMS) membranes) where E_(t)=E_(b)=1 MPa, thefirst membrane 302 thickness can be approximately 0.8 mm and the secondmembrane 304 thickness can be approximately 0.3 mm (or even 0.15 mm). Anaperture radius can be approximately 18 mm, and a piston 310 radius canbe approximately 17 mm with a thickness of approximately 4 mm. Thesecond membrane 304 radius can be approximately 20 mm. Therefore, thecalculation results in a required piston displacement of approximately0.64 mm and a piston force of approximately 0.12 N (or equivalent to aweight of 12 grams). An additional 4.6 grams are required to produce amaximum deflection of the lens surface on the first membrane 302 ofδ_(t=)1.3 mm, thus the total actuator force is 16.6 grams.

In one example, glycerol is used as the optically transparent liquidbecause it has both high refractive index (n=1.47) and does not swellPDMS membranes (e.g., the first and second membranes 302 and 304). For aliquid lens filled with glycerol, with density of 1.26 g cm⁻³, a lenswith vertical height of 36 mm can produce a maximum hydrostatic pressuredifference of P_(hyd)=g·ρ_(g)·h=444.5 Pa between inside and outside thefluidic chamber. Therefore, if glycerol is inserted into the chamber atatmospheric conditions, the first membrane 302 can bulge significantlyoutward, which makes the initial lens optical power high. Thehydrostatic pressure drop deflection is significantly reduced if thelens reservoir is pressure equilibrated and hermetically sealed.Pressure equilibration is achieved when the lens cavity/chamber isfilled in by bath immersion, in this case in a mixture of 3:2 glyceroland water, such that at any given point pressure inside and outside thelens are almost equal thus producing little deformation of the membranes302 and 304 during the fill operation. To obviate these issues, twoholes can be drilled on the annular sealing rim (e.g. frame wall) forinsertion of the optical lens fluid and venting of air. The two holescan be hermetically sealed while the lens is submerged. The lens is nextpulled out of the glycerin bath, rinsed and dried. The hermetic sealproduces a vacuum head pressure that counteracts fluid motion driven bygravity producing a much smaller lens deformation. After sealing of thelens chamber, a 1 mm thick acrylic washer can be attached to the frontside of the lens (e.g., adjacent the first membrane 302). A second 0.5mm thick washer can be attached to the back side (e.g., adjacent thesecond membrane 304) with raised supports for the bimorph actuators.

In one example, the lens (e.g., variable focus optical device) consistsof a rigid annular sealing rim (e.g., frame 314) of thickness, γencapsulated by the first and second membranes 302 and 304 forming thesealed chamber 306. The first membrane 302 has uniform thickness, t_(t)and radius, r_(t). The second membrane 304 has a rigid flat centralpiston 310 of radius, r_(p) supported by a flexible annular membrane ofthickness, t_(b) and radius, r_(b). The thickness of the second membrane304 is made very thin (0.15-0.3 mm) such that the force required to flexit is negligible compared to that required to deform the first membrane302. When a force is applied to the piston 310, the shape of the firstmembrane 302 changes bulging out or in depending on the direction of theforce, as further discussed above. The radius of the entire variablefocus optical device 300 is defined by the frame 314 and the lensthickness is defined by the piston displacement required for a givenoptical power change. The deflection requirement depends on the shape ofthe first membrane 302.

The first membrane 302 deflection, u_(o) for a circular membrane ofconstant thickness under radial tension T and uniform pressure q_(o)satisfies the modified biharmonic equation,

D·Λ ⁴ u _(o) −T·Λ ² u _(o) =q _(o).  (17)

Here, D is the flexural rigidity of the first membrane 304. Theequations of D and T are,

$\begin{matrix}{{D = \frac{E \cdot t_{t}^{3}}{12( {1 - \mu^{2}} )}},{T = {ɛ_{i} \cdot E \cdot t_{t}}},} & (18)\end{matrix}$

where ε_(i) is the initial membrane stretch, E is the membrane Youngmodulus, and μ is the membrane Poisson's ratio. The solution of equation(1) for any T and D for a circular diaphragm with clamped edge boundaryconditions is well known:

$\begin{matrix}{{u_{o} = {\frac{q_{o} \cdot r_{t}^{2}}{4 \cdot T}\lbrack {( {1 - \rho^{2}} ) + {\frac{2}{\beta \cdot {I_{1}(\beta)}}( {{I_{o}( {\beta \rho} )} - {I_{o}(\beta)}} )}} \rbrack}},} & (19)\end{matrix}$

where I₀( ) and I₁( ) are the zero and first order modified Besselfunctions of the first kind,

$\beta = {r_{t} \cdot \sqrt{\frac{T}{D}}}$

is the normalized ratio of tension over rigidity, and

$\rho = \frac{r}{r_{t}}$

is the normalized diaphragm radius. This solution has two well-knownlimits for tension and rigidity dominated regimes. The maximumdeflection height, h at the membrane center (r=0) is

$\begin{matrix}{{h = {{u_{o}(0)} = {\frac{q_{o} \cdot r_{t}^{2}}{4 \cdot T}\lbrack {1 + \frac{2( {1 - {I_{o}(\beta)}} )}{\beta}} \rbrack}}}.} & (20)\end{matrix}$

Note that, if tension is very large (β>>1), equation (4) converges to,

${h = \frac{q_{o} \cdot r_{t}^{2}}{4T}}.$

In order to form a liquid lens, a spherical surface of radius ofcurvature R is desired. Though, the deformed membrane is not fullyspherical, one must approximate the deflection as a quadratic in pcorresponding to a spherical cap of radius R and maximum height h, where

(R−h)² +r _(t) ² =R ².  (21)

For typical lenses used for eyewear h<<r_(t), hence R=r_(t) ²/2h. Thusthe lens optical power is,

$\begin{matrix}{{{P_{opt}( q_{o} )} = {{\frac{( {n - 1} )}{R} \approx \frac{2{h( {n - 1} )}}{r_{t}^{2}}} = {\frac{q_{o}}{2 \cdot T}{( {n - 1} )\lbrack {1 + \frac{2( {1 - {I_{o}(\beta)}} )}{\beta \; {I_{1}(\beta)}}} \rbrack}}}}.} & (22)\end{matrix}$

The lens power is thus proportional to the pressure, q_(o). The firstmembrane 302 displaced volume is the volume of the spherical cap,

ΔV _(front)(q _(o))=⅙πh(3r _(t) ² +h ²)≈½πhr _(t) ².  (23)

Since the chamber volume is fixed the same liquid volume is displaced bythe second membrane 304. If the second membrane 304 is thin and narrow(e.g., 0.3 mm) and of negligible rigidity,

$\begin{matrix}{{{{\Delta {V_{back}( q_{o} )}} \approx {\frac{1}{2}\pi {d_{p}( {r_{b}^{2} + r_{p}^{2}} )}}} =  {{\Delta {V_{front}( q_{o} )}} \approx {\frac{1}{2}\pi hr_{t}^{2}}}\Rightarrow{h \approx {\frac{( {r_{b}^{2} + r_{p}^{2}} )}{r_{t}^{2}}d_{p}}} },} & (24)\end{matrix}$

where d_(p) is the piston displacement. The piston force is, F=πr_(b)²q_(o). Combining equation (6) and equation (8), one obtains expressionsfor the piston spring constant k_(p),

$\begin{matrix}{k_{p} = {\frac{F}{d_{p}} \approx {4\pi \; {T \cdot \frac{r_{b}^{2}( {r_{b}^{2} + r_{p}^{2}} )}{r_{t}^{4}}}{\frac{1}{\lbrack {1 + \frac{2( {1 - {I_{o}(\beta)}} )}{\beta \; {I_{1}(\beta)}}} \rbrack}.}}}} & (25)\end{matrix}$

Thus the optical power versus piston displacement,

$\begin{matrix}{{{P_{opt}( d_{p} )} \approx {2( {n - 1} )\frac{( {r_{b}^{2} + r_{p}^{2}} )}{r_{t}^{4}}d_{p}}}.} & (26)\end{matrix}$

At the default lens position, the two membranes 302 and 304 are flat andthe minimum rim gap is selected such that the membranes are not incontact for the largest piston displacement, or γ_(min)≈d_(p). Thisrelation defines the minimum volume and weight of liquid in the chamberas a function of the maximum lens power such that

$\begin{matrix}{{V_{liquid} \geq \frac{\pi \cdot r_{t}^{2} \cdot P_{\max}}{2( {n - 1} )}}.} & (27)\end{matrix}$

Equations (25), (26), and (27) are useful to estimate some of the liquidlens parameters. For example, for an optical power change of +3D withglycerol as the optical fluid and using first membrane 302 radius of 18mm, piston radius of 16 mm, and bottom membrane radius of 20 mm, therequired piston displacement is 0.511 mm which is also the minimum gap.The minimum glycerin volume is thus ≈1.3 cm³. For glycerin with density,ρ_(o)=1.26 g/cc, this corresponds to a minimum liquid weight of 1.64 gr.Practically speaking, the lens weight can also be affected by thethickness and weight of the frame.

The force required to move the piston also depends on the initialtension parameter, T The first and second membranes 302 and 304 can bemade of polydimethylsiloxane (PDMS) with thicknesses of 1.2 mm and 0.2mm, respectively, and in one example. The Young modulus and tension ofthese membranes can vary significantly depending on the PDMS mixtureformulation and curing cycle. These parameters can be measured using thedeflection method described in Yang et al. (Q. Yang, P. Kobrin, C.Seabury, S. Narayanaswamy, and W. Christian, “Mechanical modeling offluid-driven polymer lenses,” Applied Optics 47(20), 3658-3668 (2008)).The value of Young's modulus, Poisson's ratio, and pre-strain were 987.6kPa, 0.49, and 2.83%, respectively. This pre-strain yields a pre-tensionof 33.5 N/m. The calculated piston force required at the highest opticalpower (+3 D) was 0.75N or 76 gm consistent with these parameters.

The deformation of the first membrane 302 is not only subject to thepiston force but also the effects of gravity. If the lens is standingupright on its edge, gravity produces hydrostatic pressure whichincreases linearly from the top to the bottom of the lens. Thishydrostatic pressure adds to that of the piston thus producing anon-spherical deformation and asymmetric bulging of the diaphragm. Thislens shape distortion produces a significant amount of coma aberrationthat must be minimized for acceptable optical performance. Thedeformation of membranes under symmetric hydrostatic pressure is givenas

$\begin{matrix}{{u_{h} = {\frac{\rho_{o}g\; r_{t}^{3}\cos {\theta ( {1 - \rho^{2}} )}}{8T}\lbrack {1 - \frac{2( {{I_{1}(\beta)} - {I_{2}( {\rho \beta} )}} )}{{\beta ( {1 - \rho^{2}} )}{I_{2}(\beta)}}} \rbrack}},} & (28)\end{matrix}$

where g is the gravitational acceleration (9.8 m/s²), θ is the anglerespect to the vertical axes, and I₂( ) is the second order modifiedBessel functions of the first kind. The hydrostatic pressure produces anS-type deflection that adds to the symmetric deflection of equation (3).The net effect of the distortion is that the optical power at the top islower than at the bottom of the lens (when the lens is vertical, as wornby a wearer). The slope of the distorted lens power at its center can becalculated from the mean curvature of equation (28) as,

$\begin{matrix}{ \frac{\partial P_{opt}}{\partial r} \rceil_{r = 0} \approx {\frac{\rho_{o}g}{2 \cdot T}{{( {n - 1} )\lbrack {1 - \frac{\beta^{2}}{8{I_{2}(\beta)}}} \rbrack}.}}} & (29)\end{matrix}$

For T=33.54 N/m and aperture radius of 16 mm, considering 80% radius ofthe maximum aperture, the variation of the optical power from the centerof the first membrane 302 is about ±1 D. This variation adds to thepiston-driven power of equation (26). The calculated and measured slopesof the optical power at the center of the lens are 0.084 D/mm and 0.1D/mm respectively. The power uniformity and quality of the lens imagehowever can be arbitrarily improved if the tension is increased at theexpense of a larger piston force which can also be implemented.

There are several ways to digitally control the piston deflection andlens power. A simple effective and always stable scheme uses slidingmode control (SMC). In SMC for each of the three bimorph actuators onecan incorporate a displacement sensor. of the lens the microcontrollercalculates the displacement error Ek and the rate of change of the errorIf the actuators are controlled by pulse width modulator signals, thePWM duty cycle is set to PWM=f(ε_(k)). If the frequency response of theactuators is much smaller than that of the control PWM signals, thisresults in averaging of the PWM signal to produce very smooth control ofthe actuator displacement and lens power.

In the examples of FIGS. 1-3C, the lens aperture can be 32 mm while thepower required to actuate the piston can be less than 100 mW, and insome cases, between 10 and 20 mW. The assembled lens unit can also bevery lightweight, such as approximately 15 grams, because of theimplementation of curved bimorphs, which can weigh less than 1 gram eachfor a 32 mm aperture lens, thereby resulting in a 42 mm diameter lens,for instance. Such lens can have a total thickness of approximately 8.4mm, a total weight of approximately 16 grams, and an optical range of5-7 diopters. This is a dramatic improvement over existing systems thatrequire much more power and weight to change a focal length of a muchsmaller lens aperture (e.g., 10 mm or less).

FIG. 4 illustrates smart eyeglasses 400 having a pair of variable focusoptical devices 402 (i.e., lenses), such as described with reference toFIGS. 1-3C, in accordance with an example of the present disclosure. Inone aspect, the eyeglasses 400 can comprise a frame 406 supporting abattery 408, a microcontroller 410, an object distance sensor (412 a,bor 414), and an optional pair of eye tracking sensors 416. At a minimum,a single object distance sensor 414 can be used. Alternatively, multipledistance sensors can be used to increase accuracy. The microcontroller410 can be supported within the frame and electrically coupled to thebattery 408 and to each of the variable focus optical devices 402, theobject distance sensor (412 or 414), and the pair of eye trackingsensors 416. The battery 408 can be an 8 gm 110 mAh LiPo battery that isrechargeable via a port in the frame 406, for instance. The componentson FIG. 4 are shown schematically for illustration purposes, but as willbe appreciated from below, the components are selected for theirrelative size and power capabilities to form lightweight smart glasses.

The microcontroller 410 can be operatively coupled to each variablefocus optical devices 402 to control a focal length of each lens, asfurther discussed above. Any suitable low-power microcontroller may beused. The microcontroller 410 can optionally have a wireless interfacethat wirelessly communicates with an external computer system, such as asmart phone or tablet via a Bluetooth, BLE (or other wireless protocol)connection. Thus, a custom developed software application (for androidand iOS devices) can be configured to control the focal point of thelenses 402 by causing the microcontroller 410 to actuate respectivepistons according to a particular focal length desired based on adistance to an object viewed by the wearer and a user baseline focallength or his eyeglass prescription. Alternatively, the microcontroller410 can be programmed to control a focal length of each variable focusoptical devices 402. The app is used to upload user settings such as theeyewear prescription. The type of vision defect (farsightedness,nearsightedness, and other types), as well as parameters related to thespeed of the control loop (how often the adaptive lenses are updated),distance measuring options, filtering options, extended battery lifeoptions, and various other types of parameters. The microcontroller canalso be used to store the weared vision behavior such as the distance tothe object over time. This data can be stored in the microcontroller andlater downloaded by the app from the set microcontroller.

In one example, the object distance sensor can comprise a camera 412 aand a laser 412 b mounted on either side of the frame 406, in oneaspect. The camera 412 a can be a subminiature CCD or CMOS camera suchas the Awaiba Naneye and the Omnivision camera cube families, and thelaser 412 b can be mounted such that its laser beam is congruent withthe line of sight of the wearer. The laser 412 b can illuminate a smallspot on an object (e.g., the dog), and the spot is recorded on thecamera. The location of the spot is a function of the object distance.Laser triangulation distance measurement systems are very common, andwork well over extended distances of several hundred meters.

In an alternative example, the object distance sensor can comprise anultrasonic transducer 414 that sends acoustic pulses to an object andthen used to “listen” to an echo from the sound reflection on theobject. The object distance is equal to the echo time (or time of flight“TOF”) divided by twice the speed of ultrasound. Commercial ultrasonicdistance sensors can resolve distances of 1 mm over a range of 5 m.Thus, the object distance sensor 414 can be a TOF distance sensor basedon light. Infrared based TOF rangers can be used for distancemeasurement and 3D mapping of objects. For example, ST Micro producesmicroelectronics (VL6180X, VL53L0X). The entire TOF subsystem is lessthan 5 mm in length but is capable of measuring distances up to 5 m witha nominal 5 mW power dissipation. Other non-limiting examples includeusing Intel's Realsense and Infineon (IRS10x0c) TOF depth cameras.

In conjunction with the object distance sensor (412 a,b or 414), theoptional eye tracking sensors 416 can be utilized to determine whichobject being viewed while the distance sensor determines its distancefrom the eyeglasses 400. Eye tracking sensors can improve autofocusingperformance to focus on desired objects. Eye tracking is the process ofmeasuring either the point of gaze (where the wearer is looking) or themotion of an eye relative to the head. An eye tracker is a device formeasuring eye positions and eye movement. These sensors can be used todetermine the location of an observed object in the visual field, whichultimately is used to determine the object distance from the depthcamera data. Each eye tracking sensor 416 can comprise an infrared LEDand a miniature camera embedded in the frame 406 near the respectivelens. The reflected light (provided by the LED) from the eye can becaptured by the camera to estimate eye and the gaze angle. Based on thisinformation the gaze point can be calculated and the object distance canbe determined from the object distance sensor (412 a,b or 414).Non-limiting examples of suitable eye tracking sensors can includesubminiature CMOS cameras such as the Awaiba NanEye and Omnivisioncamera cubes.

In addition to the camera type schemes for eye tracking,electro-occulography can be utilized. This technique only requires therecording of electrode signals with electrodes placed at the nosesupport and the temples (for x axis gaze). Electrooculography (EOG) is atechnique for measuring the corneo-retinal standing potential thatexists between the front and the back of the human eye. The resultingsignal is called the electrooculogram. Primary applications are inophthalmological diagnosis and in recording eye movements. Unlike theelectroretinogram, the EOG does not measure response to individualvisual stimuli. To measure eye movement, pairs of electrodes are placedeither above and below the eye or to the left and right of the eye. Ifthe eye moves from center position toward one of the two electrodes,this electrode “sees” the positive side of the retina and the oppositeelectrode “sees” the negative side of the retina. Consequently, apotential difference occurs between the electrodes. Assuming that theresting potential is constant, the recorded potential is a measure ofthe eye's position. While the resolution of EOG is not quite as good asthat obtained by cameras due to the compactness of the technique and lowcost (only requiring a few wires), it can be readily and effectivelyimplemented with the frame 406 and microprocessor 410 for eye trackingdevices and methods. The placement of the EOG electrodes can also beconsistent with the frame 406 adjacent the nose of the wearer.

Fixed power eyeglasses cannot restore the full visual range of vision,but variable power adaptive glasses can restore the full range if thelens accommodating range is

ΔP _(lens)>(ΔP _(eye))normal−ΔP _(eye)  (30)

In the worst case possible the defective eye has zero accommodationhence ΔP_(lens)=(ΔP_(eye))_(lens)≈7-10 diopters. The lens power requiredto bring an image in focus depends on the object distance; therefore theuse of an adaptive lens can also benefit from a distance sensor, such asdescribed above.

In one example using a smartphone application, the system settings anddefault lens power can be controlled by a phone application where theuser inputs (via the application) a specific eyeglass prescriptionvector consisting of the corrective fixed powers for the left and righteyes. Once set, the prescription vector is wirelessly sent to the smarteyeglasses where it is registered. The smart glasses continuouslymeasure (and record) the distance from the lens to the object plane.Next, it calculates the required corrective lens power to bring theobject into focus and changes the adaptive lens power accordingly. Thereare several potential schemes for performing the correction. In thesimplest scheme one may assume that the observer has zero accommodationand (P_(eye))₀ is fixed. Since

$\begin{matrix}{\frac{1}{f_{o}} = {( P_{eye} )_{0} + P_{lens}}} & (31)\end{matrix}$

Therefore:

$\begin{matrix}{\frac{1}{f_{o}} = {( P_{eye} )_{0} + P_{lens}}} & (32) \\{P_{lens} = {{\frac{1}{s_{o}} + \frac{n_{i}}{s_{i}} - ( P_{eye} )_{0}} = ( {A + \frac{1}{s_{o}}} )}} & (33)\end{matrix}$

where A is a constant. Therefore, the lens power must be adjusted with a1/so dependence. Since the values of s_(i) are known, the constant A canbe determined from the eyeglass prescription vector S=(p_(l), p_(r)).For presbyopia or hyperopia, the prescription is for reading glasses,typically experimentally found to produce a comfortable sharp image at areading distance with s_(o)=d_(read)=25 cm. Therefore the adaptive lenspower obeys

$\begin{matrix}{{{\overset{harpoonup}{P}}_{lens}(d)} = {{\overset{harpoonup}{S}}_{read} + {( {\frac{1}{d} - \frac{1}{d_{read}}} ) \cdot \overset{harpoonup}{n}}}} & (34)\end{matrix}$

while for myopia prescription one can use

$\begin{matrix}{{{\overset{harpoonup}{P}}_{lens}(d)} = {{\overset{harpoonup}{S}}_{myop} + {\frac{1}{d} \cdot \overset{harpoonup}{n}}}} & (35)\end{matrix}$

Other more sophisticated relations between the lens power and objectdistance can be used to minimize the lens electrical power. For example,one may adjust the lens focus only when the eye needs it (by usingequations above) over a restricted set of distances or with an abrupt orsmoothed boundary. A significant parameter in these devices is thedistance from the lens to the object of interest. This distance can bemeasured using time-of-flight microsensors, cameras and eye trackingsensors, such as those described above. The eye tracker determines thedirection of the object. A fixed direction vector normal to the eyeglasscenter, which only requires a single TOF distance measurement, may beused in the system.

An advantage of the smart glasses is the ability to continuously recordthe visual and motional activity of the observer and its correlationsthat may be used as a measure of the eyeglasses effectiveness. Theeyeglass microcontroller (e.g., 410) can record object distance versustime as well as head elevation angle. This information can besupplemented with additional location data from its correspondingtethered phone or tablet to construct an accurate record of the observerdaily visual activities such as reading, walking, and driving. Forexample, if the visual acuity of the observer is adversely drifting, therecord will display longer and wider adjustments of reading distance ormay result in a longer response time during driving. The analysis ofthis data can be used to determine when the user may require a differentprescription setting or when to visit an eye doctor for assistance. Thelens, based on data analysis, can be configured to make adjustments tothe prescription, thus reducing needs for doctor visits.

In one test of smart eyeglasses with a human eye emulator, a phonecamera, a variable focusing lens, and a servo-driven gimbaled stage,quantitative measurements can be utilized of the clarity of the imageand the response of the adaptive glasses under various simulatedaccommodation disorders. The testing included a combination oflarge-aperture fluidic lenses, ultralight actuators, object distance andeye direction sensors, and embedded control, communications andcomputing electronics. A helmet mounted unit can be incorporated toutilize the fluidic lenses with adjustment attachments. The attachmentscan be connected to two stepper motors that adjust the lens focaldistance through a microcontroller. The distance to object measurementcan be performed with a digital ultrasonic range sensor (Maxbotix). Theentire system can be controlled using an 84 MHz Arduino Due boardconnected via a bluetooth interface. One important aspect is thedistance sensor. Ultrasonic sensors in particular are subject to manyreflections; thereby a quality distance sensor can be highly useful inminimizing distance measurement errors. Based on these observations,utilization of light-based time-of-flight sensing devices can be used.The weight and size of the components can also be commercially balanced.The speed of actuation also can be commensurate with the typical timeused in head and eye movements ˜0.5 seconds.

Adaptive liquid lenses, which are based on physical adjustment of thelens shape as discussed herein, have the advantages of intrinsic smoothinterface, adaptively tuned or reconfigured output, polarizationinsensitive, broadband, and vibration resistance (if two density-matchedliquids are employed). Some applications for such lenses includecellphone cameras, image processing, optical communication, sensors andvision devices. Various operating principles can be used, such as, butnot limited to: fluidic pressure, electrochemistry, thermal effect,environmentally adaptive hydrogel, electro-wetting, anddielectrophoresis. Among these, fluidic pressure can be the moststraightforward way to dynamically manipulate the optical interfaceformed by liquids.

The smart eyeglasses 400 are capable of recording the visual and motionbehavior of the observer to determine the eyeglass effectiveness anddegradation of the observer vision accommodation. This information canbe recorded on the microprocessor 410 and periodically downloaded to itstether phone/table for further analysis and adaptive adjustment ofprescription settings. This ata can be uploaded to an online database.The information can also be used to alert the observer when eye visionhas significantly drifted and the data could be shared with eye doctorsfor further analysis. The networking capability could also lead to smarteyeglass broadcast communications between the observer home (lightingcontrol, etc.) and ultimately vehicles and work environment computers.

Although the above smart eyeglass 400 can be particularly effective, theactuators can alternatively be driven via manual adjustments. Forexample, a simple switch or set of buttons can allow a user to manuallyincrease or decrease focal length and power. In this case, the switchcan be coupled to a limiter which connects to the actuators which arestill powered by a battery. This can decrease weight and cost comparedto the more elaborate configurations described above at a sacrifice offocusing speed.

In one image testing example (using the variable focus optical devicedescribed herein), a number of components were utilized, such as acollimated light source, a tunable neutral density filter, a mount forthe variable focus optical device, and a sophisticated Shack-Hartmannwavefront (SHS) sensor (e.g., Thor labs WFS150-7AR) connected to alaptop. The SHS sensor measures the curvature of the light wavefrontafter it passes through the variable focus optical device. It is alsocapable of measuring the aberrations of the variable focus opticaldevice via Zernike polynomial expansion coefficients. These opticalcomponents are mounted on an optical table. SHS sensors allow for therapid determination of focal lengths and lens powers without furtheradjustments of object and image distances (hence setup is fixed).

SHS sensor software can be used in testing a variable focus opticaldevice for light when the lens power is +2 (focal length 500 mm). Toevaluate lens optical performance and image quality, the lensaberrations were measured with the SHS using a 4f optical test setup.The wavelength of the collimated test light source can be 0.625 μm. Theaberration values at no actuation (0.78 D), lens convex, and concavestates are shown in the following Table 2:

TABLE 2 Optical Optical Optical Aberration power +0.8 D power +3 D power−1 D Astigmatism 45° −0.364 μm −0.354 μm 0.376 μm Astigmatism 90° −0.380μm 0.343 μm 0.400 μm Trefoil X −0.008 μm −0.035 μm −0.056 μm Trefoil Y−0.007 μm −0.385 μm 0.070 μm Coma X 0.298 μm −0.208 μm −0.153 μm Coma Y−0.7400 μm −0.264 μm −0.608 μm Spherical −0.068 μm −0.188 μm −0.119 μmRMS Aberration 0.958 μm 0.733 μm 0.846 μm

The main contributor for root-mean-square (RMS) wavefront aberration at0.78 D (no actuation) was coma. Coma aberration is proportional to thethird power of the radius of the lens and inversely proportional to themembrane tension as shown in the following equation:

$\begin{matrix}{{u_{h} = {\frac{\rho_{o}g\; r_{t}^{3}\cos \; {\theta ( {1 - \rho^{2}} )}}{8T}\lbrack {1 - \frac{2( {{I_{1}(\beta)} - {I_{2}( {\rho \beta} )}} )}{{\beta ( {1 - \rho^{2}} )}{I_{2}(\beta)}}} \rbrack}}.} & (36)\end{matrix}$

In one performance test, coma aberration was worst at no actuation andit decreased significantly at higher optical power. Spherical aberrationwas very small at no actuation and it increased a little at high opticalpower. The low values of spherical aberration are indicative of thetension dominated membrane deflection. The value of trefoil aberrationalso increased from negligible value to 0.385 μm as the lens opticalpower increased because the actuators applied forces at three differentpoints 120 degrees apart along the periphery. All these aberrationvalues except coma are relatively small and below 0.5 μm which is theapproximate RMS value of human lens aberration. The 80 percent encircledenergy radii of the point spread function (PSF) were also measured atthree different lens optical powers. The values were 0.1 degrees, 0.065degrees, 0.065 degrees at lens optical power +0.8D, +3D and −1D,respectively.

FIG. 5A is a graph of voltage vs. lens optical power, illustrating oneexample of performance results of a variable optical device (e.g., alens), such as described herein. If the voltage is applied and increasedin a positive direction to three curved bimorphs (e.g., 112 a-c) thethree bimorph actuators along with the piston (e.g., 110) move in aninward direction (e.g., FIG. 3B), as further discussed above. Fornegative voltage, the piston moves outward making the lens concave(e.g., FIG. 3C), as further discussed above. Thus, FIG. 5A, shows thelens optical power (at the lens center) as a function of actuatorvoltage. In one test, the lens has an offset power of +0.78 D (Diopters)when unpowered. The lens optical power ranged in between −2.03 D to+3.57 D for a voltage range of −250 V to +250 V, which was belowdepolarization voltage. The lens optical power is linearly proportionalwith the actuator voltage. The resulting slope can be S=13 mD/V.

FIG. 5B is a graph of electrical power (mW) vs. operating frequency(Hz), and FIG. 5C is a graph of piston deflection (mm) vs. operatingfrequency (Hz), illustrating one example of performance results of avariable optical device (e.g., as lens), such as described herein. Theelectrical power dissipation for a lens is relatively very small, in therange of 10-20 mW. This is ideal low power performance as the lenses canbe operated from lightweight rechargeable portable batteries, such aswith an 8 gm, 110 mAh LiPo battery, such that the lens can continuouslyoperate for about 6 hours and have a battery life of about 12 hours. Oneof the important advantages for piezoelectric bimorph actuators is thezero static power consumption; hence battery lifetime can besignificantly extended if the focal change frequency is reduced. Themechanical resonance of the structure/frame determines the speed ofresponse for the lens. The frequency response of the lens is measured byobserving the deflection of the lens piston (via a bouncing laser beam)projected onto a screen as a function of bimorph driving frequency. Thelens displays a resonant frequency of about 70 Hz, which is illustratedon FIG. 5C as the uppermost point on the graph. The lens can be operatedcontinuously for more than 500 cycles with the driving circuit in thevoltage range of −220 V to +220 V without observing any failure orsignificant performance degradation. It can also be actuatedintermittently for more than 6 months without any failure, in oneperformance test.

The foregoing detailed description describes the invention withreference to specific exemplary embodiments. However, it will beappreciated that various modifications and changes can be made withoutdeparting from the scope of the present invention as set forth in theappended claims. The detailed description and accompanying drawings areto be regarded as merely illustrative, rather than as restrictive, andall such modifications or changes, if any, are intended to fall withinthe scope of the present invention as described and set forth herein.

What is claimed is:
 1. A variable focus optical device, comprising: afirst membrane; a second membrane, wherein, together with the firstmembrane, the second membrane at least partially defines a chamber; anoptically transparent liquid disposed in the chamber; and at least oneactuator configured to indirectly deform the chamber upon actuation tochange a focal length of the variable focus optical device.
 2. Thedevice of claim 1, further comprising a piston coupled with at least oneof the first and second membranes.
 3. The device of claim 2, wherein theat least one actuator is configured to move the piston, and wherein thedevice is configured such that movement of the piston deforms thechamber to change a focal length of the variable focus optical device.4. The device of claim 2, wherein the piston is transparent, at least inpart.
 5. The device of claim 1, wherein the at least one actuatorcomprises a piezoelectric actuator.
 6. The device of claim 4, whereinthe at least one actuator comprises a curved bimorph actuator comprisinga passive layer and an active layer, and wherein the curved bimorphactuator is configured to both bend and rotate upon actuation.
 7. Thedevice of claim 5, wherein the at least one actuator comprises aplurality of curved bimorph actuators, and wherein each of the pluralityof curved bimorph actuators is at least substantially equally spacedapart and together the plurality of curved bimorph actuatorscircumferentially surround the chamber.
 8. The device of claim 6,wherein each of the plurality of curved bimorph actuators is coupled tothe piston with a pivoting pin.
 9. The device of claim 7, wherein thepiston comprises a plurality of piston connecting portions protrudingradially from the piston, and wherein each of the plurality of curvedbimorph actuators is coupled to the piston within a hole formed in eachof the plurality of piston connecting portions.
 10. The device of claim1, wherein the variable focus optical device comprises eyeglasses.
 11. Avariable focus optical device, comprising: a frame; a pair of lensescoupled to the frame, wherein each lens comprises: a chamber having anoptically transparent liquid disposed therein; and at least one actuatorpivotally coupled to a connecting portion and circumferentiallypositioned about the chamber, wherein the at least one actuator isconfigured to deform the chamber upon actuation to change a focal lengthof the lens.
 12. The variable focus optical device of claim 11, whereinthe at least one actuator comprises a plurality of curved bimorphactuators.
 13. The variable focus optical device of claim 11, furthercomprising a piston, wherein the connecting portion extends from thepiston.
 14. The variable focus optical device of claim 11, wherein theat least one actuator is pivotally coupled to the connecting portionwith a pivoting pin extending in a hole.
 15. A pair of smart eyeglasses,comprising: a frame; a pair of lenses coupled to the frame, wherein eachlens comprises: a chamber having a transparent liquid disposed therein;and at least one actuator positioned adjacent to a periphery of thechamber, wherein the at least one actuator is configured to deform thechamber upon actuation to change a focal length of the lens; an objectdistance sensor coupled to the frame and configured to measure adistance from the eyeglasses to an object; and a microcontroller coupledto the frame and operatively coupled to the object distance sensor,wherein the microcontroller is configured to facilitate actuating the atleast one actuator to adjust a focal length of each lens according todata received from the object distance sensor.
 16. The smart eyeglassesof claim 15, wherein the at least one actuator is pivotally coupled tothe chamber.
 17. The smart eyeglasses of claim 16, wherein the at leastone actuator is indirectly pivotally coupled to the chamber.
 18. Thesmart eyeglasses of claim 16, further comprising at least one connectingportion, wherein each actuator of each of the at least one actuator ispivotally coupled to a connecting portion of the at least one connectingportion, and wherein each connecting portion of the at least oneconnecting portion is coupled to the chamber.
 19. The smart eyeglassesof claim 17, further comprising a piston, wherein each connectingportion of the at least one connecting portion extends from the piston.20. The smart eyeglasses of claim 18, wherein the at least one actuatorcomprises a plurality of curved bimorph actuators, wherein each of theplurality of curved bimorph actuators is at least substantially equallyspaced apart and together the plurality of curved bimorph actuatorscircumferentially surround the chamber, and wherein each of theplurality of curved biomorph actuators is pivotally coupled to aconnecting portion of the piston by way of a pivoting pin.